Introduction
In.1: A perspective on Hilbert's Programs
In.2: Milestones
I. Mathematical roots
I.3: Dedekind's analysis of number
I.4: Methods for real arithmetic
I.5: Hilbert's programs: 1917-1922
II. Analyses
Historical
II.1: Finitist proof theory: 1922-1934
II.2: After Königsberg
II.3: In the shadow of incompleteness
II.4: Gödel at Zilsel's
II.5: Hilbert and Bernays: 1939
Systematical
II.6: Foundations for analysis and proof theory
II.7: Reductions of theories for analysis
II.8: Hilbert's program sixty years later
II.9: On reverse mathematics
II.10: Relative consistency and accessible domains
III. Philosophical horizons
III.1: Aspects of mathematical experience
III.2: Beyond Hilbert's reach?
III.3: Searching for proofs
Wilfried Sieg is the Patrick Suppes Professor of Philosophy at
Carnegie Mellon University. He received his Ph.D. from Stanford
University in 1977. From 1977 to 1985, he was Assistant and
Associate Professor at Columbia University. In 1985, he joined the
Carnegie Mellon faculty as a founding member of the University's
Philosophy Department and served as its Head from 1994 to 2005. He
is internationally known for mathematical work in proof theory,
historical work on modern logic and mathematics, and philosophical
essays on the nature of mathematics. Sieg is a Fellow of the
American Academy of Arts and Sciences.
"Anyone who has at least a passing interest in the philosophy of
mathematics, the relatively recent history of mathematics,
mathematical logic (especially proof theory), the growth of ideas
in mathematics, or the foundations of mathematics, will find this
essential reading. Sieg is a major scholar in all of these areas,
and he has shown, throughout his career, how work in any of these
areas illuminates all of them."--Stewart Shapiro, Notre Dame
Philosophical Reviews
"Certainly mathematical logicians with a historical bent will eat
[Hilbert's Programs and Beyond] all up like candy. But others will,
too. It is, or at least should be, the case that all of us have
some awareness of the controversies of the early 20th century and
the role they played in bringing about the shape of contemporary
mathematics. ... To revisit these themes and explore certain of
their facets in great detail is a beneficial and pleasant
experience." --MAA Reviews
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